State Standards: GLEs/GSEs National Content Standards:
Grade Span Expectations [Math]:
M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems. M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems. M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:
• Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways.
• Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation).
• Formulate and redefine problem situations as needed to arrive at appropriate conclusions.
Grade Span Expectations [Physics]:
PS3 (7-8) 8: Students demonstrate and understanding of motion by… (8a)… measuring the distance and time for a given moving object and using those values to calculate speed. (8b)… Solving for any unknown in the expression v=d/t given values for the other two variables. (8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by… (8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs. (8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by… (8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object. (8bb)… Using a quantitative representation of the path of an object that has both horizontal and free fall motion. (8cc)… Modeling, illustrating, graphing, and or quantitatively explaining the path of an object that has both horizontal and free fall motion.
Context of the Lesson Where does this lesson fit in the curriculum and instructional context? Is it the opening of a unit or a series of lessons?
This lesson was designed to be one of the first lessons of the projectile motion unit. It is the first lesson in which the students are exposed to the idea of working in 2 different directions at once. It is also the first time that they will be exposed to the idea that a bullet shot and a bullet dropped will hit the ground at the same time (i.e. the x and y directions are independent).
NOTE: The lesson is designed to be taught during a block that lasts 80-90 minutes. For shorter blocks, this lesson can be broken up into two pieces.
Prior to this lesson, students should be proficient with working with objects moving in one direction. They should fully understand the concepts of position, velocity, and acceleration and should be able to use the 3 basic kinematics equations to solve problems regarding motion in one dimension. They should also be able to solve problems that deal with objects in free fall. Aside from this perquisite knowledge students should also have been exposed to trigonometric ratios (discussed in lesson 1) and should be able to break a vector into its x and y components. They should also have a solid mathematical foundation and should be able to manipulate equations involving 1 or 2 unknowns. They should also be able to solve systems of linear equations.
Opportunities to Learn
Differentiation: Materials, Learners and Environments
Plans to differentiate instruction: In order to differentiate my instruction throughout this lesson I have split the lesson up into several different segments each of which contains different types of instruction. The first segment involves a teacher demonstration followed by a class discussion. The second segment involves watching a video that relates to the teacher demonstration and this is also followed by a class discussion. The third segment involves a student investigation in which they work in groups to achieve a common goal. And the final segment involves the groups presenting their findings to the class. This lesson includes several different forms of instruction so as to maximize the learning experience for all of my students. It is constantly changing so that the students will stay engaged in the lesson and won’t become bored. I have developed this lesson to appeal to all types of learners including those who learn visually and kinesthetically. In addition to this, throughout the lesson I will have “extra” challenges for the advanced students. In the sections to follow I will explain how I will ask the advanced students probing questions to make them consider the concepts in more detail. This will allow them the opportunity to challenge themselves and not have any “dead” time during the lesson. For the students that may be struggling I will offer them guiding questions and assistance throughout the student investigation. I have detailed these guiding questions in the next section. Accommodations and modifications: In order to accommodate for the different learners in my classroom I will group the students so that they are working with students of similar levels. Therefore they can all work at their own pace and the advanced students won’t have to wait for the struggling students and the struggling students won’t seem threatened or intimidated by the more advanced students. Environment factors: When performing a mini lab it is important to consider where the groups will be positioned in the room and where the materials will be located so as to be easily accessible to all of the students. It is also important to position the groups so that the instructor can properly manage the classroom during the investigation. The lab that will be performed during this lesson involves shooting small projectiles will elastic bands. In order to minimize the danger of this activity I will position the groups in the four corners of the rooms. Therefore they can shoot their projectiles into the corner rather than out into the center of the room. I will also position all of the materials in bins on the lab bench at the front of the classroom, which will help to preserve the flow of the lesson. Materials: ü Myth Busters video clip (http://www.youtube.com/watch?v=D9wQVIEdKh8) ü Measuring Tapes/ Rulers ü Elastic Bands ü Small Balls/ projectiles ü Stopwatches ü Large paper
Objectives
Students will design and implement an investigation in which they successfully find experimental support of the fact that motion in the x and y directions are independent of one another.
Instructional Procedures
LAUNCH A:
The students will enter the classroom and I will have already posted the days agenda on the front/side whiteboard so that we can refer back to the agenda over the course of the period. The students will take their seats and will begin working on the "daily question" which is the way in which I will start each and every lesson. The question for the day will be "what serves as the fasters projectile in the world?". Once the students have finished answering the daily question and submitting their answers I will begin with the lesson
The first part of this lesson is designed to engage the students and challenge their previously held beliefs. I will perform a very simple experiment involving dropping a marble and shooting a marble horizontally at the same time. “We are going to start the day with a small demonstration.” I will stand up on a chair at the front of the classroom and address the students.
“If I were to drop a marble from this height and then I were to throw a marble horizontally as hard as I can, which marble would take less time to hit the ground?”
I will allow the students to engage in a small discussion about this idea and they will all come to a conclusion. I will not challenge their views but rather I will use a small apparatus that is designed to fire a marble sideways and drop another marble at the same time. The students will see that the marbles strike the ground at the same time.
“Why do you think this happens? How could it be that the marbles strike the ground at the same time? What if I fired the marble harder and it had a greater initial velocity?”
This should spark another class discussion and then I will ask them what would happen if a bullet was fired and another bullet was dropped from the same height.
“What if I fired a gun and dropped a bullet at the same time?”
“What if I fired a gun and dropped a basketball at the same time?”
Once we have discussed these ideas together as a class I will explain that Myth-busters had an episode that tested this exact idea. I will play a short 2-minute video in which the guys from myth-busters actually provide experimental data that backs up this concept of independent directions.
After the video we will discuss the results as a class and I will ask them if they are convinced. I will explain that many times I am not convinced in something until I try it out myself. I will assign them groups and will challenge them to develop an investigation in which they find experimental support for the “bullet shot/ dropped” theory.
“I would like for each group to develop a procedure in which they test out the idea that a projectile launched horizontally from a given height will strike the ground at the same time as a projectile that is dropped from that same height. You will then implement this procedure and explain your results. The purpose of this investigation is for you to convince yourselves that this idea is real!”
However, prior to allowing them to begin to work on this investigation I will review the safety procedures. I will explain to the students that whenever they are working with projectiles there is a danger that they projectile could end up striking someone in their eyes. I will not tolerate students throwing the projectiles around the room and I will explain to them that if I see this they will be immediately removed from the room. I will also explain to them that they must roll/ shoot their projectiles (off the table) into a corner or towards an exterior wall rather than out into the middle of the classroom where other students could trip or possibly be injured.
EXPLORE A:
I will explain to the class the instructions and will show them the different materials that I have gathered for them to use. They will be allowed to choose from a variety of different balls (Basketballs, tennis balls, racquet balls) and can also use meter sticks (which they can set up as ramps/ tracks on the table in order to get the ball moving before it leaves the table.
Each group will convene at a different lab bench and there will be a small whiteboard at each station. They will have to discuss together how they wish to go about the investigation and what materials they want to use. They will outline their ideas on the whiteboard and will have to have me check over the procedure before they can collect the materials and begin the lab.
If groups are having trouble with the task I will offer some guidance:
“What is it exactly that you are trying to show?”
“Does it matter whether we drop the ball and shoot the ball simultaneously?”
“What do we need to keep constant during this investigation?”
“If we change timers are we being consistent? Will we still get accurate results?”
“How can we improve the precision of our measurements?”
“How can we make sure that one of the balls is projected perfectly horizontally?”
If groups seem to find the mini lab too easy I will have questions to challenge them a little further.
“If we drop a basketball and shoot a marble will they hit the ground at the same time? Why?”
“If we don’t fire the projectile perfectly sideways what happens?”
“If the ball is bouncing before it leaves the edge of the table, is it really projected horizontally?”
The students will need to create their own table to record their measurements in and they must show through their data that the two projectiles hit the ground at the same time. The idea is that the will create a track of some sort on their table which will allow the ball to pick up speed and then level off and leave the edge of the table without bouncing. I will try to guide them towards this experimental set up in the process.
SUMMARIZE/SHARE A:
I will have the students record their results and their procedure on the small whiteboards and I will walk around the room to talk to each group about their findings and explain to them that the following class period they will be presenting their results to the class. I will instruct them to decide who will talk about what and I will have them draw a diagram to go along with their results.
As I walk around the room to each group I will ask them some questions to assess their understanding of the concepts:
“Why do you think that you got the results that you got?”
“If we don’t fire the projectile perfectly sideways what happens?”
“What does this tell us about the x and y directions of an objects motion?”
“How do you think that this is going to help us as we move forward with this unit?”
“What did the guys in myth-busters do that was similar to you?”
“What did they do that was different?”
“If you had more advanced technology (anything that you can think of), how would you improve this lab to make it more accurate?”
These questions will allow me to gauge their understanding of the content as well as their ability to create and implement scientific investigations (i.e. the scientific method).
I will then have the class reconvene and I will explain to the students that this phenomenon happens because the motion of an object in the x and y directions are completely independent of one another. I will explain that this idea is fundamental to the study of projectile motion and that we will be referring to it regularly in the future. I will also connect the day’s investigation to the myth busters video and explain that what the guys did in the video was essentially exactly the same as what the students did in the classroom (except they had some fancier equipment).
I will end the class by asking the students if they have any additional questions and will remind them that they will be presenting their results and their findings to the class the following class period.
Assessment
In order to assess my students during this investigation I will determine whether each student has successfully completed each of the objectives described above.
Explore A:
During the investigation I will assess the students informally on their understanding of the content of the lesson. I will observe each of the groups during this investigation and I will ask them the questions that I have detailed above. Based on their responses to my questions I will determine if they understand exactly what they are trying to figure out. I will keep a journal during the class period and record notes about each student in the class. I want to make sure that they students grasp the idea of independent directions because otherwise the projectile motion unit will be compromised. If they don’t understand this idea they won’t be able to successfully complete the tasks that will appear in the coming lessons. No grades will be assigned to the students but I will observe their participation in their groups and make sure that everyone is engaged.
Summarize A:
During the summarize phase of this investigation I will be able to individually talk to each of the students. By doing this I will be able to further gauge how well they understand the concepts and the “bullet shot/ dropped” theory. I will also be able to determine how well the students are able to apply the scientific method and how well they are able to work cooperatively in groups.
Reflections This section to be completed only if lesson plan is implemented.
Lesson Implementation: Was not able to implement this lesson yet.
Lesson Title
Independent Directions: Mini Lab!
National Content Standards:
M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems.
M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems.
M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:
• Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways.
• Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation).
• Formulate and redefine problem situations as needed to arrive at appropriate conclusions.
Grade Span Expectations [Physics]:
PS3 (7-8) 8: Students demonstrate and understanding of motion by…
(8a)… measuring the distance and time for a given moving object and using those values to calculate speed.
(8b)… Solving for any unknown in the expression v=d/t given values for the other two variables.
(8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by…
(8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs.
(8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by…
(8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object.
(8bb)… Using a quantitative representation of the path of an object that has both horizontal and free fall motion.
(8cc)… Modeling, illustrating, graphing, and or quantitatively explaining the path of an object that has both horizontal and free fall motion.
Where does this lesson fit in the curriculum and instructional context? Is it the opening of a unit or a series of lessons?
NOTE: The lesson is designed to be taught during a block that lasts 80-90 minutes. For shorter blocks, this lesson can be broken up into two pieces.
Prior to this lesson, students should be proficient with working with objects moving in one direction. They should fully understand the concepts of position, velocity, and acceleration and should be able to use the 3 basic kinematics equations to solve problems regarding motion in one dimension. They should also be able to solve problems that deal with objects in free fall. Aside from this perquisite knowledge students should also have been exposed to trigonometric ratios (discussed in lesson 1) and should be able to break a vector into its x and y components. They should also have a solid mathematical foundation and should be able to manipulate equations involving 1 or 2 unknowns. They should also be able to solve systems of linear equations.
Differentiation: Materials, Learners and Environments
In order to differentiate my instruction throughout this lesson I have split the lesson up into several different segments each of which contains different types of instruction. The first segment involves a teacher demonstration followed by a class discussion. The second segment involves watching a video that relates to the teacher demonstration and this is also followed by a class discussion. The third segment involves a student investigation in which they work in groups to achieve a common goal. And the final segment involves the groups presenting their findings to the class.
This lesson includes several different forms of instruction so as to maximize the learning experience for all of my students. It is constantly changing so that the students will stay engaged in the lesson and won’t become bored. I have developed this lesson to appeal to all types of learners including those who learn visually and kinesthetically.
In addition to this, throughout the lesson I will have “extra” challenges for the advanced students. In the sections to follow I will explain how I will ask the advanced students probing questions to make them consider the concepts in more detail. This will allow them the opportunity to challenge themselves and not have any “dead” time during the lesson.
For the students that may be struggling I will offer them guiding questions and assistance throughout the student investigation. I have detailed these guiding questions in the next section.
Accommodations and modifications:
In order to accommodate for the different learners in my classroom I will group the students so that they are working with students of similar levels. Therefore they can all work at their own pace and the advanced students won’t have to wait for the struggling students and the struggling students won’t seem threatened or intimidated by the more advanced students.
Environment factors:
When performing a mini lab it is important to consider where the groups will be positioned in the room and where the materials will be located so as to be easily accessible to all of the students. It is also important to position the groups so that the instructor can properly manage the classroom during the investigation. The lab that will be performed during this lesson involves shooting small projectiles will elastic bands. In order to minimize the danger of this activity I will position the groups in the four corners of the rooms. Therefore they can shoot their projectiles into the corner rather than out into the center of the room. I will also position all of the materials in bins on the lab bench at the front of the classroom, which will help to preserve the flow of the lesson.
Materials:
ü Myth Busters video clip
(http://www.youtube.com/watch?v=D9wQVIEdKh8)
ü Measuring Tapes/ Rulers
ü Elastic Bands
ü Small Balls/ projectiles
ü Stopwatches
ü Large paper
Instructional Procedures
The students will enter the classroom and I will have already posted the days agenda on the front/side whiteboard so that we can refer back to the agenda over the course of the period. The students will take their seats and will begin working on the "daily question" which is the way in which I will start each and every lesson. The question for the day will be "what serves as the fasters projectile in the world?". Once the students have finished answering the daily question and submitting their answers I will begin with the lesson
The first part of this lesson is designed to engage the students and challenge their previously held beliefs. I will perform a very simple experiment involving dropping a marble and shooting a marble horizontally at the same time.
“We are going to start the day with a small demonstration.”
I will stand up on a chair at the front of the classroom and address the students.
“If I were to drop a marble from this height and then I were to throw a marble horizontally as hard as I can, which marble would take less time to hit the ground?”
I will allow the students to engage in a small discussion about this idea and they will all come to a conclusion. I will not challenge their views but rather I will use a small apparatus that is designed to fire a marble sideways and drop another marble at the same time. The students will see that the marbles strike the ground at the same time.
“Why do you think this happens? How could it be that the marbles strike the ground at the same time? What if I fired the marble harder and it had a greater initial velocity?”
This should spark another class discussion and then I will ask them what would happen if a bullet was fired and another bullet was dropped from the same height.
“What if I fired a gun and dropped a bullet at the same time?”
“What if I fired a gun and dropped a basketball at the same time?”
Once we have discussed these ideas together as a class I will explain that Myth-busters had an episode that tested this exact idea. I will play a short 2-minute video in which the guys from myth-busters actually provide experimental data that backs up this concept of independent directions.
After the video we will discuss the results as a class and I will ask them if they are convinced. I will explain that many times I am not convinced in something until I try it out myself. I will assign them groups and will challenge them to develop an investigation in which they find experimental support for the “bullet shot/ dropped” theory.
“I would like for each group to develop a procedure in which they test out the idea that a projectile launched horizontally from a given height will strike the ground at the same time as a projectile that is dropped from that same height. You will then implement this procedure and explain your results. The purpose of this investigation is for you to convince yourselves that this idea is real!”
However, prior to allowing them to begin to work on this investigation I will review the safety procedures. I will explain to the students that whenever they are working with projectiles there is a danger that they projectile could end up striking someone in their eyes. I will not tolerate students throwing the projectiles around the room and I will explain to them that if I see this they will be immediately removed from the room. I will also explain to them that they must roll/ shoot their projectiles (off the table) into a corner or towards an exterior wall rather than out into the middle of the classroom where other students could trip or possibly be injured.
EXPLORE A:
I will explain to the class the instructions and will show them the different materials that I have gathered for them to use. They will be allowed to choose from a variety of different balls (Basketballs, tennis balls, racquet balls) and can also use meter sticks (which they can set up as ramps/ tracks on the table in order to get the ball moving before it leaves the table.
Each group will convene at a different lab bench and there will be a small whiteboard at each station. They will have to discuss together how they wish to go about the investigation and what materials they want to use. They will outline their ideas on the whiteboard and will have to have me check over the procedure before they can collect the materials and begin the lab.
If groups are having trouble with the task I will offer some guidance:
“What is it exactly that you are trying to show?”
“Does it matter whether we drop the ball and shoot the ball simultaneously?”
“What do we need to keep constant during this investigation?”
“If we change timers are we being consistent? Will we still get accurate results?”
“How can we improve the precision of our measurements?”
“How can we make sure that one of the balls is projected perfectly horizontally?”
If groups seem to find the mini lab too easy I will have questions to challenge them a little further.
“If we drop a basketball and shoot a marble will they hit the ground at the same time? Why?”
“If we don’t fire the projectile perfectly sideways what happens?”
“If the ball is bouncing before it leaves the edge of the table, is it really projected horizontally?”
The students will need to create their own table to record their measurements in and they must show through their data that the two projectiles hit the ground at the same time.
The idea is that the will create a track of some sort on their table which will allow the ball to pick up speed and then level off and leave the edge of the table without bouncing. I will try to guide them towards this experimental set up in the process.
SUMMARIZE/SHARE A:
I will have the students record their results and their procedure on the small whiteboards and I will walk around the room to talk to each group about their findings and explain to them that the following class period they will be presenting their results to the class. I will instruct them to decide who will talk about what and I will have them draw a diagram to go along with their results.
As I walk around the room to each group I will ask them some questions to assess their understanding of the concepts:
“Why do you think that you got the results that you got?”
“If we don’t fire the projectile perfectly sideways what happens?”
“What does this tell us about the x and y directions of an objects motion?”
“How do you think that this is going to help us as we move forward with this unit?”
“What did the guys in myth-busters do that was similar to you?”
“What did they do that was different?”
“If you had more advanced technology (anything that you can think of), how would you improve this lab to make it more accurate?”
These questions will allow me to gauge their understanding of the content as well as their ability to create and implement scientific investigations (i.e. the scientific method).
I will then have the class reconvene and I will explain to the students that this phenomenon happens because the motion of an object in the x and y directions are completely independent of one another. I will explain that this idea is fundamental to the study of projectile motion and that we will be referring to it regularly in the future. I will also connect the day’s investigation to the myth busters video and explain that what the guys did in the video was essentially exactly the same as what the students did in the classroom (except they had some fancier equipment).
I will end the class by asking the students if they have any additional questions and will remind them that they will be presenting their results and their findings to the class the following class period.
Explore A:
During the investigation I will assess the students informally on their understanding of the content of the lesson. I will observe each of the groups during this investigation and I will ask them the questions that I have detailed above. Based on their responses to my questions I will determine if they understand exactly what they are trying to figure out. I will keep a journal during the class period and record notes about each student in the class. I want to make sure that they students grasp the idea of independent directions because otherwise the projectile motion unit will be compromised. If they don’t understand this idea they won’t be able to successfully complete the tasks that will appear in the coming lessons. No grades will be assigned to the students but I will observe their participation in their groups and make sure that everyone is engaged.
Summarize A:
During the summarize phase of this investigation I will be able to individually talk to each of the students. By doing this I will be able to further gauge how well they understand the concepts and the “bullet shot/ dropped” theory. I will also be able to determine how well the students are able to apply the scientific method and how well they are able to work cooperatively in groups.
This section to be completed only if lesson plan is implemented.